Abstract
The infinite root boundary does not exist because of m < n . Finally, the complex root boundary (CRB) is obtained by equating the real and imaginary parts of Pi(jw) to zero. In this case, Equation (4) is returned to two equations
Highlights
SWITCHED systems are a category of hybrid systems composed of different sub-systems and a switching rule specifying the active sub-system in the timetable. [1,2,3]
A switched system with some unstable sub-systems may exhibit a stable behavior with the switching operation [4]
The stability regions using the fractional order PI controller for each sub-systems are obtained separately by Neimark’s D-partition method [16]. This region includes the fractional order PI controller parameters that stabilize their sub-systems. Plotting these stability regions on a same graph, the common stability region of fractional order PI controller which makes the overall switched system stable are obtained by intersecting these stability regions
Summary
SWITCHED systems are a category of hybrid systems composed of different sub-systems and a switching rule specifying the active sub-system in the timetable. [1,2,3]. The switched systems and their control with single fractional order PI controller is investigated. The objective of the control is to obtain all stabilizing set of fractional order PI controllers for the overall switched system rather than better performance. The stability regions using the fractional order PI controller for each sub-systems are obtained separately by Neimark’s D-partition method [16]. This region includes the fractional order PI controller parameters that stabilize their sub-systems Plotting these stability regions on a same graph, the common stability region of fractional order PI controller which makes the overall switched system stable are obtained by intersecting these stability regions. An important advantage of the method is that the designer eliminates the controllers which make the overall switched control system unstable
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